Respuesta :
You can use this rule to find any even natural number. Multiply the position of the number by 2 to find the number. In this example, you would take 100 times 2 to get 200. I used the given pattern to figure this out. 2 x 2 = 4, 2 x 3 = 6, 2 x 4 = 8, 2 x 5 = 10, etc....
Answer: The 100th even natural number is 200.
Step-by-step explanation: Given that the following arithmetic sequence represents the set of natural numbers :
2, 4, 6, 8, 10, . . ..
We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.
We know that
the n-th term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
For the given sequence, we have
a = 2 and d = 4 - 2 = 6 - 4 = . . . =2.
Therefore, the 100-th term of the sequence will be
[tex]a_{100}=a+(100-1)d=2+99\times2=2+198=200.[/tex]
Thus, the 100th even natural number is 200.
